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A093121 A Jacobsthal Fibonacci product. 1
1, 0, 4, 6, 30, 80, 286, 882, 2924, 9350, 30438, 98208, 318278, 1029210, 3331820, 10780014, 34888062, 112894960, 365344142, 1182264930, 3825911596, 12380874550, 40065409014, 129654294336, 419570260150, 1357757640330 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
Form a graph from a triangle and its midpoint triangle. A093121 counts closed walks of length n at a vertex of the midpoint triangle in this configuration.
LINKS
FORMULA
G.f.: (1-x-3x^2)/((1+x-x^2)(1-2x-4x^2));
a(n)=A078008(n)*A000045(n+1);
a(n)=(2^n/3+2(-1)^n/3)(((1+sqrt(5))/2)^(n+1)/sqrt(5)-((1-sqrt(5))/2)^(n+1)/sqrt(5)).
MATHEMATICA
LinearRecurrence[{1, 7, 2, -4}, {1, 0, 4, 6}, 30] (* Harvey P. Dale, Aug 26 2019 *)
CROSSREFS
Sequence in context: A046849 A090530 A154667 * A248048 A209298 A075590
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Mar 22 2004
STATUS
approved

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Last modified February 29 10:50 EST 2024. Contains 370425 sequences. (Running on oeis4.)